A jetliner can fly 5.57 hours on a full load of fuel. Without any wind it flies at a speed of 2.43 x 102 m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 49.9-m/s wind from the jet stream, which blows from west to east. What is the maximum distance (in kilometers) that the plane can travel due west and just be able to return home?

Question

A jetliner can fly 5.57 hours on a full load of fuel. Without any wind it flies at a speed of 2.43 x 102 m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 49.9-m/s wind from the jet stream, which blows from west to east. What is the maximum distance (in kilometers) that the plane can travel due west and just be able to return home?

Answer 1

Vp = 243m/s * (1/1000)km/m * 3600s/h =

875km/h. = Velocity of plane.

Vw = 49.9m/s * (1/1000)km/m * 3600s/h =
180km/h = Velocity of the wind.

d1 = d2,
(875-180)t = (875+180)(5.57-t),
695t = 1055(5.57-t),
695t = 5876.35 - 1055t,
695t + 1055t = 5876.35,
1750t = 5876.35,
t = 3.36h.

d = Vt = 695 * 3.36 = 2334km.,max.

Answer 2

To determine the maximum distance the plane can travel due west and still be able to return home, we first need to calculate the time it takes to fly west and east separately.

Let's start with the time it takes to fly due west.

The plane's speed without wind is 2.43 x 10² m/s. However, it encounters a wind speed of 49.9 m/s blowing from west to east. To determine the effective speed of the plane (considering the wind), we subtract the wind speed from the plane's speed.

Effective speed of the plane = Plane's speed - Wind speed
Effective speed = 2.43 x 10² m/s - 49.9 m/s

Now, let's calculate the time it takes to fly west.

Time to fly west = Distance / Effective speed

To determine the distance, we need to multiply the time by the plane's flight duration on a full load of fuel. The given flight duration is 5.57 hours or 5.57 x 3600 seconds.

Distance = Time to fly west x Flight duration

Now let's calculate the distance:

Distance = (Time to fly west) x (Flight duration)
Distance = (Time to fly west) x (5.57 x 3600)

Next, we need to calculate the time it takes to fly east.

The effective speed when flying east will be the sum of the plane's speed and the wind speed. This is because the wind is blowing from west to east, so it will provide a boost when flying in that direction.

Effective speed of the plane while flying east = Plane's speed + Wind speed
Effective speed = 2.43 x 10² m/s + 49.9 m/s

Now, let's calculate the time it takes to fly east:

Time to fly east = Distance / Effective speed

Again, we need to multiply the time by the plane's flight duration to determine the distance.

Distance = (Time to fly east) x (Flight duration)

Now let's calculate the distance:

Distance = (Time to fly east) x (Flight duration)
Distance = (Time to fly east) x (5.57 x 3600)

Finally, to find the maximum distance that the plane can travel due west and return home, we need to set the distance flown west equal to the distance flown east:

(Time to fly west) x (5.57 x 3600) = (Time to fly east) x (5.57 x 3600)

We can cancel out the flight duration from both sides of the equation:

Time to fly west = Time to fly east

Now, we can substitute the equations for the time to fly west and east respectively:

(Distance / Effective speed while flying west) = (Distance / Effective speed while flying east)

We can cancel out the distance from both sides of the equation:

1 / (Effective speed while flying west) = 1 / (Effective speed while flying east)

Substituting the expressions for the effective speeds:

1 / (2.43 x 10² - 49.9) = 1 / (2.43 x 10² + 49.9)

Now, we can solve this equation to find the value of the maximum distance that the plane can travel due west and return home.

Answer 3

To find the maximum distance that the plane can travel due west and still be able to return home, we need to consider the effect of wind on the plane's ground speed in both directions.

First, let's calculate the ground speed of the plane when flying westward against the wind. We subtract the wind speed from the plane's airspeed:

Ground speed against the wind = Airspeed - Wind speed
= (2.43 x 10^2 m/s) - (49.9 m/s)
= (2.43 x 10^2 - 49.9) m/s
= 193.1 m/s

Next, let's calculate the ground speed of the plane when flying eastward with the wind. We add the wind speed to the plane's airspeed:

Ground speed with the wind = Airspeed + Wind speed
= (2.43 x 10^2 m/s) + (49.9 m/s)
= (2.43 x 10^2 + 49.9) m/s
= 292.9 m/s

Now, we can calculate the maximum time the plane can fly due west and still have enough fuel to return home. We divide the total flight time (5.57 hours) by 2 since the plane needs to spend equal time flying in each direction:

Maximum time flying due west = Total flight time / 2
= 5.57 hours / 2
= 2.785 hours

Next, let's calculate the maximum distance the plane can travel due west:

Maximum distance flying due west = Maximum time flying due west * Ground speed against the wind
= 2.785 hours * (193.1 m/s)
= 537.7935 kilometers

Therefore, the maximum distance the plane can travel due west and still be able to return home is approximately 537.7935 kilometers.